Quantum Dephasing in a Gated GaAs Triple Quantum Dot due to Nonergodic Noise

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Quantum Dephasing in a Gated GaAs Triple Quantum Dot due to Nonergodic Noise

M. R. Delbecq, T. Nakajima, P. Stano, T. Otsuka, S. Amaha, J. Yoneda, K. Takeda, G. Allison, A. Ludwig, A. D. Wieck, and S. Tarucha

Phys. Rev. Lett. 116, 046802 – Published 26 January 2016

Abstract

We extract the phase coherence of a qubit defined by singlet and triplet electronic states in a gated GaAs triple quantum dot, measuring on time scales much shorter than the decorrelation time of the environmental noise. In this nonergodic regime, we observe that the coherence is boosted and several dephasing times emerge, depending on how the phase stability is extracted. We elucidate their mutual relations, and demonstrate that they reflect the noise short-time dynamics.

Received 2 December 2015

DOI:https://doi.org/10.1103/PhysRevLett.116.046802

Physics Subject Headings (PhySH)

Noise Quantum information with solid state qubits

Quantum dots

Nuclear magnetic resonance

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

M. R. Delbecq^1,*, T. Nakajima¹, P. Stano^1,2, T. Otsuka¹, S. Amaha¹, J. Yoneda¹, K. Takeda¹, G. Allison¹, A. Ludwig³, A. D. Wieck³, and S. Tarucha^1,4

¹Center for Emergent Matter Science, RIKEN, 2-1 Hirosawa, Wako-shi, Saitama 351-0198, Japan
²Institute of Physics, Slovak Academy of Sciences, 845 11 Bratislava, Slovakia
³Lehrstuhl für Angewandte Festkörperphysik, Ruhr-Universität Bochum, D-44780 Bochum, Germany
⁴Department of Applied Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan

^*matthieu.delbecq@riken.jp

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Vol. 116, Iss. 4 — 29 January 2016

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Images

Figure 1
(a) SEM micrograph of a similar device to the one measured. Lateral gates defining quantum dots (bottom) and charge sensors (top) are shown in light grey on the dark grey surface of the GaAs substrate. The three leftmost quantum dots are formed and manipulated while the upper left charge sensor, connected to an rf-reflectometry circuit is used. The “ $C$ -shaped” light colored area denotes the micromagnet providing inhomogenous magnetic field. An external magnetic field $B_{z}^{ext} = 0.7 T$ is applied. (b) Charge stability diagram in the plane defined by plunger gates $P_{1}$ and $P_{3}$ . The positions for initialization ( $I$ ), operation ( $O$ ), and measurement ( $M$ ) configurations are denoted.
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Figure 2
(a) The probability distribution of the nuclear field gradient time correlator $C_{Δ B} (Δ t)$ for acquisition time $Δ t$ from 3.8 ms (dark green) to 7.6 s (yellow). Data (dots) are fitted with a Gaussian distribution (line). Left inset: Nuclear field gradient $Δ B_{z} (t)$ extracted from the qubit frequency as a function of time. Right inset: correlator for $Δ t = 3.8 ms$ excluding (not excluding) the third spin fluctuation in green (black). (b) Variance of the nuclear field gradient correlator as a function of the acquisition time $Δ t$ . The solid line is a fit showing a growth with a power law exponent $α = 0.8$ . The dashed line shows a power law behavior with $α = 1$ for comparison.
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Figure 3
(a) Typical qubit evolution traces for different acquisition times. Solid lines are fit to decaying oscillations, giving $T_{2, ϕ}^{⋆} = 120$ , 220, and 570 ns, respectively. (b) Probability density distributions of $T_{2, ϕ}^{⋆}$ corresponding to the same acquisition times as for (a). The red solid line is a fit to a Gamma distribution resulting in skewness $γ_{1} \approx 0.75$ , and $\bar{T_{2, ϕ}^{⋆}} \approx$ as given.
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Figure 4
(a) $T_{2}^{⋆}$ from the different processings as a function of acquisition time $Δ t$ . Top inset: estimated frequencies of eight consecutive records. Averaging over all defines $T_{2, ϕ}^{⋆}$ . The correlator $σ_{B}^{2}$ is calculated from the frequency difference between the first and last record (horizontal green arrow). Postselection is performed by averaging over all blocks of records that start in a frequency window $f_{0} \pm Δ f / 2$ (upward red arrows), giving for $N = 1$ the red trace in the lower inset defining $T_{2, p s}^{⋆}$ . (In this illustration, we neglect the complication of block overlaps that can happen for $N > 1$ ). Blocks of records defining $T_{2, QC}^{⋆}$ are those of $T_{2, p s}^{⋆}$ shifted by 1 record (downward purple arrows), giving for $N = 1$ the purple trace in the lower inset. (b) Ratios $\bar{T_{2, ϕ}^{⋆}} / T_{2, B}^{⋆}$ (black squares) and $T_{2, QC}^{⋆} / T_{2, B}^{⋆}$ (purple triangles). Black dashed line (dotted black line): analytical limit for large $N$ for the mean shape ratio $k = 7.25$ (for $k \in ⟨ 6, 8.5 ⟩$ ). Purple dashed line: analytical limit for large $N$ . Purple solid line: numerical evaluation of the integral leading to Eq. (4) [26]. (c) Enhancement of $T_{2, p s}^{⋆}$ (red upwards triangles) and $T_{2, QC}^{⋆}$ (purple downwards triangles) by thresholding on the width of the estimator probability distribution peak. Inset: distribution of estimator probability peak width.
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